What is the derivative of #x*x^(1/2)#?

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Answer 1 · 2015-10-10T07:09:36

F'(x)= 2x/x^(1/2)

X^(1/2)1 +x^(-1/2)x

X/x^(1/2)+x/x^(1/2)

2x/x^(1/2)

Answer 2 · 2015-10-10T12:36:25

You could use the product rule, but might prefer to rewrite #x*x^(1/2) = x^(1+1/2)=x^(3/2)#, then use the power rule.

#d/dx(x^(3/2))= 3/2x^(3/2-1) = 3/2x^(1/2)#